Tens of thousands of Chileans marched peacefully on Thursday demanding profound changes to the country's heavily centralised and privatised form of government, though there were also clashes between small groups and the police. More than 450 people were arrested and dozens injured.

Union members, students, government workers and centre-left opposition parties took part in the final day of a nationwide two-day strike, which included four separate protest marches in the capital and demonstrations across Chile. In many areas, families grabbed spoons and spilled into the streets to join in noisy pot-banging shows of support.

President Sebastián Piñera's ministers sought to minimise the impact. Police estimated Santiago's crowds at just 50,000 and said only 14% of government workers went on strike.

Union leaders claimed 600,000 people joined demonstrations nationwide. Raúl de la Puente, president of the government employees union, said 80% of his members joined the strike, at the cost of two days' pay.

Piñera called the strike unjustified because Chile's economy is growing strong and providing more opportunities. He also said he remains open to those seeking dialogue, although his administration has refused to discuss some student and union demands, arguing the real work of reform must be done in congress.

What began three months ago as a series of isolated classroom boycotts by high school and university students demanding education improvements has grown into a mass movement calling for all manner of changes in Chile's top-down form of government.

Protesters now want increases in education and healthcare spending, pension and labour code reform, even a new constitution that would give voters the chance to participate in referendums – a form of direct democracy previously unthinkable in a country only two decades removed from a military dictatorship.

"As long as there aren't responses from the executive to the demands, this movement will continue," university student leader Camila Vallejo vowed.

Polls taken before the strike say the majority of Chileans side with the protesters, although it's unclear how the violence will affect popular sentiment.

Chile's much-praised economic model of fiscal austerity and private-sector solutions has failed to deliver enough upward mobility to a new generation, whose members see how their country compares to the rest of the world, said Bernardo Navarrete, a political analyst at the University of Santiago.

"The promise that they have made us during the military regime and during 20 years of the [centre-left] Concertation [government], and during the era of Piñera, is that education was a way to climb up in society, and the students noticed that this wasn't true," Navarrete said. "They know that Chilean universities are the most expensive places to study, that advancing in higher education depends more on the university you leave than your own merits, that success isn't guaranteed."

Some of Piñera's ministers tried to reach out to people who feel they can't afford the quality education that Chile's best private institutions provide.

The economy minister, Pablo Longueira, told a meeting of executives on Thursday about a father who told him that he could afford to send only one of his two children to college. "If this was my reality, I would be marching as well," Longueira said. "This is what we have to change in Chile."

Others in the ruling coalition took a harder line. The governor appointed by Piñera for the Biobío region, Víctor Lobos, blamed the protests on unmarried parents, saying 65% of Chilean children are now born outside marriage.

"Today Chile is a country without family. I warned this would bring social conflicts to Chile," Lobos said. "A child that doesn't receive anything, doesn't receive affection, the loving attention of a father and mother and their protection, shows up in the streets with hate."